Answer to Question #248671 in Statistics and Probability for Jenn

Question

A certain restaurant soon to be open. In the process of preparing, they have to buy appliances. A refrigerator,which cost 45,789 has a 15% chance of replacement in the first three years of purchase. The store is offering an extension of the warranty cost of 8,785 oh the refrigerator.

a. What is the expected value of the extended warranty assuming it is replaced after years?

b. will you buy the refrigerator? Why?

c. what is the mean, variance and standard deviation?

Answer 1

Solution:

(a)

Expected value$=E(X)=-45789\times 0.15+8785\times 0.85=598.9$

(b)

Yes, I will buy the refigerator because 598.9 is way much lesser than 8785.

(c)

Mean$=E(X)=598.9$

$E(X^2)=-45789^2\times 0.15+8785^2\times 0.85=380094669.4$

Variance$=\sigma^2=E(X^2)-[E(X)]^2$

$=380094669.4-(598.9)^2 \\=379735988.19$

Standard deviation$=\sigma=\sqrt{379735988.19}=19486.815$